Operator Lipschitz estimates in the unitary setting

Ayre, P.; Cowling, M.; Sukochev, F.

doi:10.1090/proc/12833

Operator Lipschitz estimates in the unitary setting
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by P. J. Ayre, M. G. Cowling and F. A. Sukochev PDF

Proc. Amer. Math. Soc. 144 (2016), 1053-1057 Request permission

Abstract:

We develop a Lipschitz estimate for unitary operators. More specifically, we show that for each $p\in (1,\infty )$ there exists a constant $d_p$ such that $\left \Vert f(U) - f(V)\right \Vert _p \leq d_p \left \Vert U - V\right \Vert _p$ for all Lipschitz functions $f: \mathbb {T} \to \mathbb {C}$ and unitary operators $U$ and $V$.

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